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Numerical algorithm for the third-order partial differential equation with three-point boundary value problem. (English) Zbl 1474.65411

Summary: A numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. Using the reproducing property and the existence of orthogonal basis in a new reproducing kernel Hilbert space, we obtain a representation of exact solution in series form and its approximate solution by truncating the series. Moreover, the uniform convergency is proved and the effectiveness of the proposed method is illustrated with some examples.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35C10 Series solutions to PDEs
35G16 Initial-boundary value problems for linear higher-order PDEs
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